document.write( "Question 837701: Rewrite the following without logarithms:
\n" ); document.write( "f) Log W = 2(logA +logW) – (log32 +2logπ+2log r+log c) \n" ); document.write( "

Algebra.Com's Answer #504724 by Theo(13342) $\"\"$ $\"About$

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document.write( "you will get the following by using the properties of logarithms.\r\n" );
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document.write( "          2 * (log(A) + log(W) is equal to:\r\n" );
document.write( "          log( (AW)^2 ) which is equal to:\r\n" );
document.write( "          log(A^2*W^2)\r\n" );
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document.write( "           log(32) + 2*log(pi) + 2*log(r) + log(c) is equal to:\r\n" );
document.write( "           log(32) + log(pi^2) + log(r^2) + log(c) which is equal to:\r\n" );
document.write( "           log (32*pi^2*r^2*c)\r\n" );
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document.write( "your equation becomes:\r\n" );
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document.write( "           log(W) = log(A^2*W^2) - log(32*pi^2*r^2*c)\r\n" );
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document.write( "this becomes:\r\n" );
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document.write( "           log(W) = log        (         A^2*W^2        )\r\n" );
document.write( "                                    ------------------\r\n" );
document.write( "                                      32*pi^2*r^2*c\r\n" );
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document.write( "this means that:\r\n" );
document.write( "                         W =              A^2*W^2        \r\n" );
document.write( "                                    ------------------\r\n" );
document.write( "                                      32*pi^2*r^2*c\r\n" );
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document.write( "this is because if log(a) = log(b), then a must be equal to b.\r\n" );
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\n" ); document.write( "\n" ); document.write( "the properties of log that were used are:\r
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\n" ); document.write( "\n" ); document.write( "log(a^b) = b*log(a)
\n" ); document.write( "log(a*b) = log(a) + log(b)
\n" ); document.write( "log(a/b) = log(a) - log(b)
\n" ); document.write( "if log(a) = log(b), then a must be equal to b.\r
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